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Research Article | Open Access

On coupled Gronwall inequalities involving a ψ-fractional integral operator with its applications

Dinghong Jiang1,2, Chuanzhi Bai1( )
Department of Mathematics, Huaiyin Normal University, Huaian, Jiangsu 223300, China
Huaiyin High School in Jiangsu Province, Huaian, Jiangsu 223002, China
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Abstract

In this paper, we obtain a new generalized coupled Gronwall inequality through the Caputo fractional integral with respect to another function ψ. Based on this result, we prove the existence and uniqueness of solutions for nonlinear delay coupled ψ-Caputo fractional differential system. Moreover, the Ulam-Hyers stability of solutions for ψ-Caputo fractional differential system is discussed. An example is also presented to demonstrate the application of main results.

Keywords

ψ-fractional operatorsgeneralized coupled Gronwall inequalitydelay ψ-Caputo fractional differential systemexistence and uniquenessUlam-Hyers stability
CLC number: 26A24, 26A33, 26D10, 34A08, 34D20, 35A23, 39B82, 47H10

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AIMS Mathematics
Volume 7 Issue 5,
May 2022
Pages 7728-7741
DOI: 10.3934/math.2022434

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Cite this article:
Jiang D, Bai C. On coupled Gronwall inequalities involving a ψ-fractional integral operator with its applications. AIMS Mathematics, 2022, 7(5): 7728-7741. https://doi.org/10.3934/math.2022434

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Received: 18 November 2021
Revised: 12 February 2022
Accepted: 14 February 2022
Published: 15 May 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)